Final answer:
Wendy's utility-maximizing point is the consumption of 4 salads and 8 smoothies for a total utility of 8, provided the marginal utility per dollar spent is the same for both items. Without knowing the specific utility function but knowing that her utility for a given combination is highest when marginal utility per dollar is equal across items, this would indeed be her utility-maximizing choice under the given budget constraint.
Step-by-step explanation:
Wendy is seeking to maximize her utility given her budget constraint of $48. With salads costing $6 and smoothies costing $3, we know she can purchase a combination of these two items within her budget. According to consumer theory, a utility-maximizing point occurs when the marginal utility per dollar for all goods is equal. Since we know that at 4 salads and 8 smoothies the marginal utility per dollar is the same for both, we can calculate the marginal utility for each item.
Let's assume Wendy gets a utility of 8 from consuming 4 salads and 8 smoothies. Without additional information on the specific utility function or the marginal utility of the items, we can't calculate the exact utility numbers for other combinations, but we can use the given marginal utility per dollar to infer the optimal choice. Since both items bring the same marginal utility per dollar spent at this level, Wendy is at a utility-maximizing point because shifting her spending toward more of one item or the other would not increase her overall utility.
To maintain the same total utility using her full budget, Wendy needs to spend all $48 while keeping the marginal utility per dollar the same. A systematic approach suggests focusing on satisfaction per dollar. Since 4 salads and 8 smoothies give her a utility of 8 and we know her marginal utility per dollar spent is the same for both items, the utility-maximizing point for Wendy under these conditions would indeed be 4 salads and 8 smoothies, matching the information already provided in the scenario.